Problem: Solve for $x$. Enter the solutions from least to greatest. $6x^2 - 30x - 84 = 0$ $\text{lesser }x = $
Explanation: $\begin{aligned} 6x^2 - 30x - 84&= 0 \\\\ 6(x^2-5x-14)&=0 \end{aligned}$ Now let's factor the expression in the parentheses. $x^2-5x-14$ can be factored as $(x+2)(x-7)$. $\begin{aligned} 6(x+2)(x-7)&=0 \\\\ x+2=0&\text{ or }x-7=0 \\\\ x=-2&\text{ or }x=7 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -2 \\\\ \text{greater }x &= 7 \end{aligned}$